Event Category: Berkeley String-Math Seminar
Martijn Kool (Rijksuniversiteit te Utrecht), “New directions in Vafa-Witten theory”
ABSTRACT: In the 1990’s, Vafa-Witten tested S-duality of N=4 SUSY Yang-Mills theory on a complex algebraic surface X by studying modularity of a certain partition function. In 2017, Tanaka-Thomas defined Vafa-Witten invariants by constructing a symmetric perfect obstruction theory on the moduli space of Higgs pairs (E,\phi) on X. The instanton contribution (\phi=0) to these invariants is the virtual Euler … Read More
Lotte Hollands (Heriot-Watt University), “Four-dimensional BPS states in the E6 theory”
ABSTRACT: BPS states in four-dimensional N=2 theories are enumerated by spectral networks on two-dimensional Riemann surfaces. Geometrically they correspond to special Lagrangian discs ending on the spectral networks, more formally they are (conjectured to be) generalised Donaldson-Thomas invariants for an appropriate CY3 category. In this talk I will give a particularly interesting example of these BPS state counts in the … Read More
Nikita Nekrasov (Stony Brook), “Super-spin-chains and gauge theories”
ABSTRACT: Bethe/gauge correspondence relates quantum integrable systems to supersymmetric gauge theories. One of the mathematical consequences of this relation is the identification of the quantum cohomology ring of certain varieties with Bethe subalgebras of quantum algebras. In this talk the two dimensional gauge theories corresponding to the Yangians of super-algebras of A type will be described. In a parallel development … Read More
Yaim Cooper (Harvard), “Severi degrees via representation theory”
ABSTRACT: The Severi degrees of P1XP1 can be computed in terms of an explicit operator on the Fock space F[P1]. We will discuss this approach and will also describe several further applications. We will discuss using Fock spaces to compute relative Gromov-Witten theory of other surfaces, such as Hirzebruch surfaces and EXP1. We will also discuss operators which calculate descendants. … Read More
Penka Georgieva (Institut de Mathématiques de Jussieu), “The local real Gromov-Witten theory of curves”
ABSTRACT: The local Gromov-Witten theory of curves studied by Bryan and Pandharipande revealed strong structural results for the local GW invariants, which were later used by Ionel and Parker in the proof of the Gopakumar-Vafa conjecture. In this talk I will report on a joint work in progress with Eleny Ionel on the extension of these results to the real … Read More
Pavel Etingof (MIT), “Cyclotomic Double affine Hecke algebras and multiplicative quiver varieties”
ABSTRACT: I’ll show that the partially spherical cyclotomic rational Cherednik algebra (obtained from the full rational Cherednik algebra by averaging out the cyclotomic part of the underlying reflection group) has four other descriptions: (1) as a subalgebra of the degenerate DAHA of type A given by generators; (2) as an algebra given by generators and relations; (3) as an algebra … Read More
Ron Donagi (University of Pennsylvania), “Non-Abelian Hodge Theory, Mirror Symmetry, and Geometric Langlands”
ABSTRACT: We will review the Geometric Langlands Conjecture, a non-abelian generalization of the theory of curves and their Jacobians. We will compare it to its arithmetic variants and discuss its overlap with homological mirror symmetry. We will then outline our program for proving GLC using non Abelian Hodge theory and Hitchin’s system. Finally, we will describe some recent results on … Read More
Hiraku Nakajima (Kavli IPMU), “Coulomb branches and their resolutions”
ABSTRACT: Coulomb branch of a 3d gauge theory is defined (after Braverman-Finkelberg-N) as the spectrum of a certain commutative ring, defined as a convolution algebra of a certain infinite dimensional variety. A variant of its definition gives a (partial) resolution, when we have the so-called flavor symmetry in the theory. We identify the resolution with smooth Cherkis bow variety for … Read More
Alexander Givental (UC Berkeley), “The adelic Hirzebruch-RR in higher genus quantum K-theory”
ABSTRACT: I will explain how the problem of expressing K-theoretic Gromov-Witten invariants in terms of cohomological ones leads to an elegant quantum-mechanical formula.